On a sheet of paper, draw and label two congruent triangles. Your triangles should be oriented differently (example: not facing the same direction). Use marks to indicate congruent segments and congruent angles (must mark 3 congruent sides and 1 congruent angle) 10/29

The order of the ________ indicates the corresponding parts! ΔABC  ΔXYZ vertices The parts of congruent triangles that “match” are called ______________. congruent parts Review from yesterday

A CB F E D In the figure, ΔABC  ΔFDE. As in a mapping, the order of the _______ indicates the corresponding parts. vertices Congruent Angles Congruent Sides  A FF  B DD  C EE AB  FD BC  DE AC  FE These relationships help define the congruent triangles.

It turns out that in certain cases all you need are three pairs of congruent parts to know that two triangles are congruent.

The following triangle congruent postulates guarantee that 2 triangles are congruent Topic is: Postulates – assume or claim to be true

In a triangle, the angle formed by two given sides is called the ____________ of the sides. included angle A B C  A is the included angle of AB and AC  B is the included angle of BA and BC  C is the included angle of CA and CB included angle

SAS Postulate If ________ and the ____________ of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent. two sides included angle A B C R S T If AC  RT and  A   R and AB  RS then ΔABC  ΔRST

R S T A B C ASA Postulate If _________ and the ___________ of one triangle are congruent to the corresponding angles and included side of another triangle, then the triangles are congruent. two angles included side If  A   R and AC  RT and then ΔABC  ΔRST  C  TT

SSS Postulate If three _____ of one triangle are congruent to _____ _____________ sides of another triangle, then the two Triangles are congruent. sides three corresponding A B C R S T If AC  RT and AB  RS andBC  ST then ΔABC  ΔRST

R S T A B C Theorem 5-4 AAS Theorem If _________ and a ______________ of one triangle are congruent to the corresponding two angles and nonincluded side of another triangle, then the triangles are congruent. two angles nonincluded side If  A   R and CB  TS then ΔABC  ΔRST  C   T and

1. Not Enough Information 2. Yes, SAS 3. Yes, ASA or AAS Are these triangles congruent? If yes, state which triangle congruence postulate guarantees that the triangle are congruent.

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